The Cost of ESG Investing - American Economic Association
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
The Cost of ESG Investing
Laura Lindsey Seth Pruitt Christoph Schiller
Arizona State University Arizona State University Arizona State University
November 30, 2021
Abstract
Even against increasing interest in socially responsible investing mandates, we
find that implementing ESG strategies can cost nothing. Modifying optimal portfolio
weights to achieve an ESG-investing tilt negligibly affects portfolio performance across
a broad range of ESG measures and thresholds. This is because those ESG measures
do not provide information about future stock performance, either in relation to risk
or mispricing, beyond what is provided by other observable firm characteristics. That
the stock market does not reflect significant equilibrium pricing of ESG information
is rationalized in a model of responsible investing wherein investors differ in which
ESG-related criteria are used to weight their portfolios.
Keywords: ESG, IPCA, tangency portfolio, portfolio tilt, responsible investing, sus-
tainable investing
11 Introduction
Over the past two decades, the amount of investment linked to ESG goals has seen tremen-
dous growth (see Bialkowski and Starks, 2016). According to the 2020 Global Sustainable
Investment Review, sustainable-investing assets reached $35.3 trillion globally at the start
of 2020, a 15% increase over 2018 to represent almost 36% of total assets under manage-
ment. Similarly, the number of signatories of the United Nations ‘Principles for Responsible
Investment’ (PRI), institutional investors committed to ESG-oriented investment decisions,
has increased from 734 to over 3000 between 2010 and 2020.
With rapidly growing demand from clients, fund managers are increasingly looking for ways
to integrate ESG goals into their investment strategies. However, the implications of doing
so on portfolio efficiency and performance are unclear. Economic theory generally argues
that, all else equal, high-ESG firms should have lower expected returns as socially-oriented
investors require less compensation for holding high-ESG firms (e.g. Fama and French, 2007;
Pedersen et al., 2020; Pastor et al., 2021b). While Fabozzi et al. (2008), Hong and Kacperczyk
(2009), Bolton and Kacperczyk (2020), and Pastor et al. (2021a) empirically document higher
risk-adjusted returns for “sin” stocks and high-carbon-emissions firms, Edmans (2011) and
Glossner (2021), among others, find that firms with higher employee satisfaction and fewer
ESG-related controversies outperform. Perhaps unsurprisingly given this mixed evidence,
many fund managers who publicly commit to responsible investment goals do little to improve
the ESG performance of their portfolios (Kim and Yoon, 2020; Brandon et al., 2021).
The aim of this paper is to study the costs of implementing an ESG-investing mandate,
and additionally investigate whether or not ESG ratings identify systematic risk exposures
or exploitable mispricing. In contrast to previous research, which has primarily relied on
long-short portfolio sorts following Fama and French (1993), we consider ESG ratings as
firm characteristics within the context of a conditional asset-pricing model, using the in-
strumented principal components analysis (IPCA) approach of Kelly et al. (2019, 2020).
Our empirical methodology allows us to bring rich conditioning information into our esti-
mates of firms’ risk exposures, and also detect what predictive information is present in ESG
scores that is distinct from other firm characteristics. Our contribution is twofold: first, we
demonstrate that the cost of following an ESG mandate is potentially quite low, as port-
folios with ESG screens perform similarly to the unconstrained tangency portfolio implied
by our model. This finding can be explained by our second result: ESG measures from
commonly-used data providers neither provide information about systematic risk exposure
nor exploitable mispricing.
2To begin with, we use scores from any of four major ESG data providers to tilt optimal
portfolios toward satisfying a range of ESG mandates.1 We construct the tilts in two steps:
in step one we use the other valuable firm information to define a profitable portfolio; in step
two we tilt the portfolio to downweight bad-ESG firms (and possibly upweight good-ESG
firms). Some of these tilts are simple screens that drop bad-ESG firms, while others are
optimal portfolios from responsible-investing models in Pedersen et al. (2020) and Pastor
et al. (2021b). We primarily focus on ESG tilts corresponding to negative and exclusion-
ary screening, as this form of ESG investment approach represents the most common ESG
mandate globally (Dimson et al., 2020).2 In all the tilts we consider, the pre-tilt portfolio
comes from the conditional factor model and is systematic.3 Many of these portfolios can be
overlaid with ESG mandates without substantially affecting profitability. Therefore we show
that the cost of ESG investing can be quite low. Pedersen et al. (2020) state that “many
investors want to own ethical companies in a saintly effort to promote good corporate be-
havior, while hoping to do so in a guiltless way that does not sacrifice returns”— our results
show that this hope can be realized.
We next broaden our focus to ask: how can ESG tilts have zero cost? To answer this
question, we investigate the role of ESG characteristics in determining either alpha or beta.
We begin by including ESG measures along with other firm characteristics and estimate
instrumented betas on aggregate factors via IPCA. We find no evidence that ESG scores
drive factor exposures.4 Next, we allow the ESG characteristics to instead drive alpha,
defined as predictable returns that are orthogonal to aggregate risk exposures, either on
their own or alongside other characteristics: regardless, we find no evidence of significant
profits. Therefore, we conclude that ESG measures do not give significant information about
either systematic risk-exposures or exploitable mispricing, when evaluated within the context
of the rich information set available to investors.
Furthermore, we connect important existing results to our conditional pricing framework. In
particular, we reconsider the results of Edmans (2011) about a specific S (social) measure,
and the results of Pastor et al. (2021a) about a specific E (environmental) measure. First, we
1
Data employed include KLD (now MSCI ESG KLD STATS), Asset4 (now Refinitiv ESG), Sustainalytics
(now Morningstar), and RepRisk.
2
Consequently, our results are less closely related to the recent literature on ESG impact and activist
investing (see e.g. Dimson et al., 2015, 2021; Hoepner et al., 2021).
3
More specifically: the screens are based on the tangency portfolios implied by the model. The Pedersen
et al. (2020) and Pastor et al. (2021b) portfolios tilt the Markowitz portfolio, and we take the covariance
matrix and mean vector from the model estimates that impose there is no alpha.
4
Our focus is on exposures to aggregate risk, and it is there that we find no role for ESG information.
Therefore our results can coexist with the results of Engle et al. (2020), who find a significant role for hedging
specific climate risks.
3reproduce both paper’s results—that these E and S measures define significant unconditional
alphas with respect to well known observable factor models (from Fama and French, 1993;
Carhart, 1997; Fama and French, 2015). Then we show that our model, with its conditional
betas, reveals that these ESG scores do not drive statistically-significant conditional alphas.
In fact, our result closely matches the main message in Pastor et al. (2021a), who document
that green-returns have occurred mostly due to random shocks to ESG concerns and find little
scope for an ESG premium in expected returns. Our conditional-model results strengthen
this conclusion.
An important aspect of our work is the large extent of ESG information we consider. Our
main results are robust to using data from different ESG providers and ESG index sub-
components. They are robust to different subsamples, for instance focusing only on the
recent sample where ESG coverage is richer and ESG concerns, perhaps, have become more
salient. The results are similar whether or not we industry-adjust the measures. The results
are similar for various choices of missing-value imputation, or when restricted to firms with
nonmissing ESG data. And while different tilting criteria (e.g. what constitutes a good-
or bad-ESG firm, what is the desired ESG level of the portfolio, etc.) can drive significant
changes to portfolio performance (as one would expect!), there is a wide range of reasonable
choices that yield minimal deviations from the profitability of non-tilted portfolios.
How can investors care about the ESG performance of firms, tilt their portfolios to reflect
ESG scores, and yet prices fail to adjust such that ESG measures predict returns? To explain
this observation, we consider the equilibrium model of Pastor et al. (2021b) and propose a
simple solution: investors use varying ESG measures. As noted above, our empirical analysis
is quite extensive across different ESG data providers and particular ESG scores, and our
main results are robust across them all. This is a testament to the fact that there are many
ways to “do ESG”. If investors do not agree on a single definition of ESG measurement,
equilibrium pricing need not reflect their ESG concerns even if all investors act on them.
We provide empirical support that ESG measures disagree, supporting this explanation.5
This part of our analysis is closely aligned with recent research documenting substantial
disagreements across ESG data providers and the resulting asset pricing implications (Berg
et al., 2020b; Avramov et al., 2021; Christensen et al., 2021; Gibson et al., 2021).
Despite extensive research, there is widespread disagreement in the literature on the return
predictability of ESG characteristics. The lack of return predictability in our model echoes
Hartzmark and Sussman (2019) who find no evidence that sustainable funds outperform
5
An alternate interpretation that the measures available to researchers are simply noise.
4non-sustainable funds, Pedersen et al. (2020) who find that the KLD ESG scores do not
significantly predict returns and carbon emissions do not yield value-weighted alphas, and
Gorgen et al. (2020) who find insignificant differences in average returns for high- and low-
carbon-emissions firms. In contrast, a long literature on so-called “sin” stocks has found a
premium for firms in industries like alcohol or tobacco.6 In a similar vein, Zerbib (2020) uses
the holdings of “green” institutional investors to show that excluded firms have a significantly
higher average returns. Glossner (2021) documents a negative Carhart (1997) alpha of -3.5%
for firms with high reputation risk using RepRisk ratings, and Baker et al. (2018) find a
positive “greenium” for green bonds relative to similar non-green municipal bonds. Giglio
et al. (forthcoming) provide a recent survey of the large and growing literature on the effects
of ESG-investing across many different asset classes.
Our paper contributes to this rapidly growing literature along several important dimensions.
First, we use IPCA to extract aggregate risks that better-capture the mean-variance-efficient
frontier, as has been argued in Kelly et al. (2019) and Kelly et al. (forthcoming). It is
crucial to have the best-possible depiction of systematic risks when we evaluate how firms’
differing ESG scores lead to differences in average returns, so as to appropriately understand
ESG’s effects if they are risk-based, rather than inappropriately attribute them to an alpha
because one’s factor model is poor. Second, we take into account a large set of other firm
characteristics, controlling for a substantial amount of the conditioning information investors
have at their disposal already in addition to ESG scores. Third, we use data from four
major ESG providers (and evaluate both aggregate and subcomponent performance) in our
empirical analysis, making our conclusions broad. Fourth–and this pertains even when we use
the same factor model as other papers—we explicitly allow for ESG measures and other firm
characteristics to drive cross-sectional and time-series variation in alphas, betas, or both.
This way we can comprehensively evaluate ESG’s role in pricing assets, and distinguish
whether a conditional risk-based or mispricing-based explanation best fits ESG’s impact on
returns. This last contribution sheds interesting new light on existing results in Edmans
(2011) and Pastor et al. (2021a).
Our paper also contributes to the literature on the costs of implementing ESG investment
mandates. Kim and Yoon (2020) and Brandon et al. (2021) document that signatories of the
UN Principles of Responsible Investment in the U.S. experience a significant increase in fund
inflows, but do not significantly increase fund-level ESG performance in their portfolios after
committing to ESG-investment goals, while also experiencing a decrease in returns (Kim and
6
Among others, Fabozzi et al. (2008), Luo and Balvers (2017), and Pedersen et al. (2020) find that non-sin
stocks earn negative CAPM and Fama and French (1993) alphas.
5Yoon, 2020). Ceccarelli et al. (2021) show that funds that received a ‘low-carbon’ label by
Morningstar in 2018 experienced significant fund inflows. While these funds outperformed
conventional funds in months with high salience of climate change risk, they offered signifi-
cantly lower diversification benefits throughout the sample. Similarly, Aragon et al. (2020)
find that university endowments receive higher donations following the adoption of socially
responsible investment (SRI) policies but exhibit greater management costs and portfolio
return volatility. Our results demonstrate how fund managers can implement a wide range
of ESG mandates without substantially compromising Sharpe ratios relative to the tangency
portfolio.
The paper proceeds as follows. Section 2 discusses the data and availability of ESG mea-
sures. Section 3 discusses the factor model estimation, how systematic and non-systematic
strategies are formed, and how ESG-mandate tilts are implemented. Section 4 presents the
results when ESG is included in estimation or instead used as a tilt, shows robustness of
those results, discusses properties of some ESG-tilted portfolios, connects to the existing
empirical literature, and discusses our results within the context of an equilibrium model.
Section 5 concludes. The Online Appendix includes additional results and robustness tests.
2 Data
2.1 Returns and firm characteristics
Our data for returns and firm characteristics are obtained from CRSP and Compustat via
the codes provided by Jensen et al. (forthcoming). We select fifty characteristics, based
on those that provide the greatest firm-month coverage, which we refer to by their names
in Jensen et al. (forthcoming). They are: market equity and assets; cash-flow vari-
ables net income, sales; pay-out ratios eqnpo 1m, eqnpo 3m, eqnpo 6m, eqnpo 12m, ni at;
change in shares chcsho 1m, chcsho 3m, chcsho 6m, chcsho 12m; valuation ratios div3m me,
div6m me, div12m me, at me, ni me, nix me, sale me, xido at; leverage ratios debt me,
netdebt me, debt at; turnover, trading, and volume variables tvol, zero trades 21d,
zero trades 126d, dolvol 126d, turnover 126d, dolvol var 126d, turnover var 126d,
zero trades 252d, bidaskhl 21d, rvolhl 21d; past return variables ret 1 0, ret 2 0,
ret 3 0, ret 3 1, ret 6 0, ret 6 1, ret 9 0, ret 9 1, ret 12 0, ret 12 1, ret 12 7; quality-
minus-junk qmj safety, qmj prof; and, other variables seas 1 1an, age, mispricing perf.
In robustness checks, we restrict attention to a subset of these that are “slow”, defined as
66000
All firms
Large
KLD
5000 Asset4
Sustainalytics
RepRisk
4000
Number of firms
3000
2000
1000
0
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Figure 1: Available observations
having a low time-series volatility—this excludes all of the past-return variables, some trad-
ing variables, and most valuation ratios. These slow characteristics are: market equity,
div3m me, div6m me, div12m me, qmj safety, tvol, dolvol 126d, zero trades 252d, age,
assets, net income, qmj prof, ni at, debt me, netdebt me, sales, and sale me.
In order to estimate IPCA we require a firm-month observation to have all lagged charac-
teristics and the month’s return to be nonmissing. Figure 1 reports the time-series of the
number of all firms’ observations as the solid black line. As will shortly become evident, it
is useful to also restrict attention to a sample of large firms. To do so, we obtain NYSE
breakpoints from Ken French’s data library and define the large-firm cut-off as the median.
The number of large firm observations is plotted in Figure 1 as the dashed red line.
2.2 ESG characteristics
We obtain data on firm-level ESG scores from four major data providers commonly used by
investors and in the academic literature (see e.g. Berg et al., 2020b; Huang et al., 2021). Our
first data source is MSCI ESG KLD STATS (KLD), which is available from 1992 to 2018.
7KLD was the original provider of socially responsible investing information in North America
and continues to be widely used in academic settings given its length of coverage. For each
covered firm, KLD evaluates “strengths” and “concerns” across the following six dimensions
of ESG: environmental impact, community relations, product characteristics, employee re-
lations, diversity, and governance. KLD has changed its methodology and underlying data
items several times since 1992. We follow Akey et al. (2021) in accounting for these changes
and construct time-consistent scores by identifying data items that covered the same issues
but changed names over time and retaining only data items with continuous coverage since
1992. The score for each category and the overall score are then calculated as the number
of strengths minus the number of concerns. We summarize community relations, product
characteristics, employee relations, and diversity as the “social” category, as is standard in
the literature.
Second, we construct ESG scores using data from Asset4 (now Refinitiv ESG).7 Asset4
coverage starts in 2003 and includes ESG information based on over 250 key performance
indicators and over 750 individual data points, across three “pillars”: ‘E’ (emissions, resource
use, product innovation), ‘S’ (product responsibility, community, human rights, diversity and
opportunity, employment quality, health & safety, training and development) and ‘G’ (board
functions, board structure, compensation policy, vision and strategy, shareholder rights).
In a survey of investors by SustainAbility, this source was noted for its raw, quantitative
data.8 ESG “pillar” scores as reported by Asset4 are constructed by comparing firms’ ESG
measures to peers and weighting by materiality. To avoid comparability issues and put
our ESG scores on equal footing, we instead construct E, S, and G scores and an overall
ESG score by aggregating over the corresponding raw data items (equal-weighting) as in
Dyck et al. (2019).9 This also helps us address concerns about changes in the Asset4 data
aggregation methodology throughout our sample period (Berg et al., 2020a).
Third, we obtain ESG scores from Sustainalytics (now Morningstar). Sustainalytics con-
structs ESG scores based on hundreds of individual data items according to a proprietary
weighting scheme. We obtain the E, S, and G category scores as well as the aggregated
overall ESG score for the sample period from 2009 to 2017. In the SustainAbility investor
survey, Sustainalytics was mentioned as one of the most high-quality and useful providers.
7
Our Asset4 data was downloaded in 2019 and is therefore unaffected by the recent changes due to
backfilling documented by Berg et al. (2020a).
8
“Rate the Raters 2020” available at https://www.sustainability.com/thinking/rate-the-raters-2020/.
9
Following Dyck et al. (2019), for questions where a “yes” answer is associated with better ESG perfor-
mance (positive direction), we translate the Y/N items into 0 (N) and 1 (Y), and the answers to double
Y/N questions into 0 (NN), 0.5 (YN or NY), and 1 (YY). For questions with a negative direction we use a
reversed coding scheme. We normalize numerical data items to be between 0 and 1.
8Fourth, we obtain ESG data from RepRisk, which is available to us for the sample period
from 2007 to 2019. RepRisk uses both algorithms and analysts to monitor company-specific
news events related to 28 ESG issues (e.g. air pollution, product controversies, discrimi-
nation, and labor practices) using over 80,000 public sources in 20 languages such as print
and social media, regulators, think tanks, and newsletters. The company advertises its
transparency of methods and the external nature of its sources, which provide a counter-
point to providers relying primarily on company-provided data. Based on the occurrence of
ESG-related controversies, RepRisk provides a Reputation Risk Rating (RRR) using a letter
rating (AAA to D). We translate this letter scale to a numerical scale (ranging from 1 to 10
in one-unit increments) such that a higher number indicates a better rating.
The ESG measures from the four data providers are reported at different frequencies. In
particular, KLD and Asset4 ESG scores are reported annually, while Sustainalytics and
RepRisk scores are available at the monthly frequency. For the latter, timing them is quite
simple: they are in the investor’s information set at the end of that month in which they are
reported. But the former are tougher to definitively time. In fact, this issue is quite similar
to the well-known issue of timing firms’ accounting variables for the purpose of portfolio
sorting, for instance as done by the seminal Fama and French (1993)—therefore we adopt
their well-known convention. If a KLD or Asset4 score is given for year y, we assume that
it is observed by the investor starting in June of year y + 1 and remains constant for the
subsequent twelve months.
2.3 ESG coverage and summary statistics
The availability of our ESG measures varies tremendously over the sample period, as Figure
1 makes plain. The KLD measures (black dashed-dot line) are available starting in 1992 for a
small number of firms, with noticeable increases in coverage in 1996, 2002, and particularly
2004. Asset4 measures (gray dashed-dot line) start in 2004, again for a small number of
firms, and with a noticeable increase in coverage in 2016. RepRisk (gray dotted line) starts
in 2007 with relatively large coverage that gradually declines over time. Sustainalytics (black
dotted line) starts in 2009 with a small number of firms, bumps up in 2010, and remains
steady. This issue of ESG score availability is one we take seriously by a variety of means.
Figure 2 illustrates that ESG coverage is related to firm size, reported on a log scale. In
each panel, percentiles of the distribution of all available firms is reported by gray lines: the
minimum and maximum (p0 and p100 , respectively) as dotted lines at the top and bottom,
the p10 and p90 as dashed lines closer to the middle, and the median p50 as a solid line. In
9Panel A. KLD Panel B. Asset4
100 tril. 100 tril.
1 tril. 1 tril.
Market capitalization ($)
Market capitalization ($)
10 bil. 10 bil.
100 mil. 100 mil.
1 mil. 1 mil.
10 th. 10 th.
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Panel C. Sustainalytics Panel D. RepRisk
10
100 tril. 100 tril.
1 tril. 1 tril.
Market capitalization ($)
Market capitalization ($)
10 bil. 10 bil.
100 mil. 100 mil.
1 mil. 1 mil.
10 th. 10 th.
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Figure 2: Firm size and ESG availabilityaddition, the NYSE-median large-firm cut-off is plotted as the red dashed line. The gray
and red lines are identical in every panel. What changes between panels are the blue lines,
which plot the percentiles of the size distribution of firms for which that provider’s ESG
score is nonmissing. As with the gray lines, we use dotted lines for p0 and p100 , dashed-dot
lines for p10 and p90 , and a solid line for p50 .
Figure 2 broadly says that ESG coverage is skewed towards large firms. We see this plainly
for the KLD data in Panel A. For about the first ten years, the median firm with a KLD
rating is as big as the 90th percentile of all firms, judging by the relationship of the solid
blue line to the top gray dashed-dot line. A bit less than 90% of the KLD firms are above
the NYSE median, judging from how the bottom blue dashed-dot line hovers below the red
dashed line. The increases in coverage in 1996 and 2002 do little to change these facts, but
the large expansion in 2004 noticeably drops the 10-50-90 percentiles, implying increased
coverage of small firms. Nonetheless, throughout its history the KLD percentiles lie above
the percentiles of all firms, showing us the ESG coverage is better for larger firms.10
The remaining panels show that this feature is also true for other ESG providers. The largest
90% of Asset4 firms are larger than the median of the firm size distribution for almost its
entire history, with this p10 line lying above the NYSE median for the most part. The
median of Sustainalytics firms lies just below the p90 of all firms, and the 10th percentile of
Sustainalytics firms is just about at the NYSE median. And for RepRisk, half of its firms
are above the NYSE median and its distribution is consistently skewed towards large firms.
The broad takeaway here is that firms which receive ESG coverage tend to be bigger. Hence,
we will have a paucity of ESG information in the sample of all firms. For this reason, our main
results restrict attention to the sample of large firms, defined as those larger than the NYSE
median. This reduces the impact of imputing ESG scores when we do so. Furthermore, Kelly
et al. (2019) show that systematic-investment performance is lower in large firms, which we
also observe in our data. Therefore large firms provide a more-stringent test of systematic
strategies’ profitability and the impact of ESG scores thereupon. Nevertheless, sensitivity
analysis will confirm that our main results are robust to instead using the panel of all firms.
10
The top gray and blue dotted lines always lie on top of each other, for all providers. This says that all
providers have always covered the largest firms in our data.
113 Model and Portfolio Construction
In this section we briefly describe IPCA and model-implied investment strategies. We then
discuss various ways of using ESG ratings within the IPCA model, as well as using model-
implied ESG implementation strategies as a tilt.
3.1 Basic and modified IPCA models
The basic IPCA model is
′
rn,t+1 = αn,t + βn,t ft+1 + εn,t+1 , where αn,t = Γ′α zn,t and βn,t = Γ′β zn,t , (1)
for the K × 1 exposure βn,t to the K × 1 factors ft+1 , and the L × 1 firm characteristics
zn,t . The timing says that βn,t is known before ft+1 , which follows arbitrage-pricing theory.
Following Kelly et al. (2019), we refer to (1) as an unrestricted model, and a restricted
model is one where we impose Γα = 0. By estimating Γβ we allow firm characteristics to
give information on how a stock’s exposure to aggregate factors varies both cross-sectionally
and over time. The factors f could be jointly estimated along with Γβ , or instead the factors
could be exogenously specified as portfolio returns representing systematic risk. In either
case, Γβ is estimated by a large panel regression of stock returns on the interaction of factor
realizations and lagged firm characteristics. Following Kelly et al. (2019), we stack rn,t+1 into
′
the vector rt+1 and zn,t into the Nt × L matrix Zt , so we can concisely state the first-order
conditions upon which one iterates until convergence to the least-squares estimates:
−1
ft+1 = Γ′β Zt′ Zt Γβ Γ′β Zt′ (rt+1 − Zt Γα ) (2)
T −1
!−1 T −1 !
X Xh i′
vec(Γ̃′ ) = Zt Zt ⊗ f˜t+1 f˜t+1
′ ′
Zt ⊗ f˜t+1 rt+1
′
(3)
t=1 t=1
where for the restricted model we impose Γα = 0 and define Γ̃ ≡ Γβ and f˜t+1 ≡ ft+1 ,
while for the unrestricted model we instead allow a nonzero Γα and define Γ̃ ≡ [Γα , Γβ ]
′ 11
and f˜t+1 ≡ 1, ft+1
′
. Following Kelly et al. (2019), in the unrestricted model we impose
the identification assumption Γ′α Γβ = 0 meaning that risk loadings “explain as much of the
asset’s mean returns as possible”. Then Γα ̸= 0 means that there is a predictable part of
returns unrelated to aggregate risk, which we refer to as mispricing.
11
Empirically the number of stocks varies, hence the notation Nt .
12Kelly et al. (2019) and Kelly et al. (forthcoming) use this model to describe stock and bond
returns, respectively, and find unprecedented success by a variety of measures.12 Further-
more, they find that estimating f leads to significant gains, relative to instead exogenously
taking the factors as well-known portfolios (such as Fama and French, 2015; Hou et al., 2015,
amongst others). Kelly et al. (2021) emphasizes a key point: an element of Γβ is nonzero
only to the extent that the corresponding characteristic meaningfully drives differences in a
return’s covariance with aggregate risk. Hence, we construct a systematic investment when
we base the portfolio weights on βn,t even when characteristics are part of the picture.
On the other hand, when we allow Γα ̸= 0 then we are admitting a non-systematic investment
strategy to be formed. This is due to two reasons. First, we follow Kelly et al. (2019) and
impose that Γα and Γβ are orthogonal: thus, αn,t contains characteristic information that is
orthogonal to systematic exposure. Second, the timing of (1) means that αn,t is known before
the return rn,t+1 . Therefore, αn,t represents an anomaly: a predictable return that is not
compensation to aggregate risk. Kelly et al. (2019) find that Γα is statistically insignificant
in stocks (and Kelly et al., forthcoming, finds the same in bonds), therefore argue that the
restricted model best fits the data. But, those papers do not include ESG measures or
consider an ESG-investing mandate. Moreover, using the Jensen et al. (forthcoming) data
allows us to look at stock performance in recent years (the data in Kelly et al., 2019, ends
in 2014), which could be important if ESG-investing’s salience has increased over time.
3.2 Systematic investment strategies
Systematic investment strategies are based only on stocks’ aggregate risk exposures βn,t
estimated in the restricted IPCA model. Theoretically, the mean-variance-efficient frontier
is provided by the tangency portfolio constructed from systematic-risk factors. Indeed, the
stock evidence in Kelly et al. (2019) and Kelly et al. (2021), and bond evidence in Kelly
et al. (forthcoming), suggest that IPCA-based tangency portfolios are very profitable.
Suppose that the factors have excess return mean m and covariance S, which we take as
static for simplicity. Then the K × 1 factor -tangency portfolio weights are
1
wf actan = ′ −1
S −1 m (4)
ιK S m
for a K × 1 ones vector ιK . Meanwhile, the IPCA-model-implied factor weights are the
′
projection onto betas. That is, stack βn,t into the N × K matrix βt , and the K × N factor
12
Kelly et al. (2020) provide asymptotic analysis of the estimator.
13weights are h i
−1
Wf,t = (βt′ βt ) βt′ ≡ wf,1,t · · · wf,K,t (5)
where wf,k,t is the portfolio weight for the k th factor. Therefore, the 1×Nt tangency portfolio
weights combine (4) and (5):
′
wtan,t = wf′ actan Wf,t (6)
3.3 Using ESG as a tilt
There are several terms we could use to convey this section’s main idea: tilt, overlay, adjust-
ment, screen etc. The main idea is that ESG measures are not used in the estimated model,
but instead to achieve an ESG mandate. In all of the ESG tilts we consider, we constrain
our attention to systematic portfolios.
Our first method of implementing an ESG mandate is to screen firms based on ESG scores
using a simple two-step approach. First, we find the tangency portfolio weights utilizing
all non-ESG-related information via IPCA. Second, we tilt the tangency-portfolio weights
using an ESG measure—downweighting stocks with “bad” ESG information, and retaining
stocks with “good” ESG information. The result is final portfolio weights. By doing the
two steps separately, we accomplish two goals. First, we use profit maximizing weights that
are familiar and easy to describe—see Section 3.2. This is useful because we want to use
transparent machinery so as to make the ESG-investing costs clear. Second, we can consider
a variety of choices for step two and see how they impact profitability while achieving an
ESG-investing mandate.
When we tilt the investment strategy using ESG scores, we confront the reality that the scores
can be missing for many firms. We consider two main ways of dealing with this issue. First,
we include all of the available firms and adjust weights only for those with nonmissing ESG
measures that satisfy some criteria. Alternatively, we restrict attention only to firms with
nonmissing ESG measures. In addition, we must take a stand on what defines an acceptable
level of ESG performance. In our empirical analyses, we consider different percentile cut-offs
(p75 , p50 , p25 ) to gauge the effects of more- or less-stringent ESG mandates.
Two of our tilts include all of the available firms. In the first screen we exclude any firm
with an unacceptable ESG measure, defined as below the stated percentile. Of course, this
requires that we actually observe a firm’s ESG score, and therefore any firm with missing
ESG is unaffected. This tilt accomplishes the mandate: Avoid taking any position in firms
with unacceptable ESG measures. The second screen is similar to the first, but further only
14excludes stocks that would otherwise be in the long-leg of the portfolio. This tilt accomplishes
the mandate: Avoid going long in firms with unacceptable ESG measures.
The third screen restricts attention only to firms with nonmissing ESG measures. We only
include the firm in the portfolio if its ESG score is acceptable, defined as equal-to or above the
stated percentile. Hence, both firms with unacceptable ESG scores and firms with missing
ESG scores are excluded. This tilt accomplishes the mandate: Take positions only in firms
with acceptable ESG measures.
In addition to screened tangency portfolios, we construct the optimal portfolios derived by
Pedersen et al. (2020) and Pastor et al. (2021b) (for which we use the shorthand PFP and
PST, respectively)—these take into account firms’ expected returns, covariances, and ESG
information. They are similar to the tilts we just defined, because they can be seen as tilts
to the usual Markowitz weights. We simply repeat those papers’ expressions, adjusting the
notation for our explicitly conditional context.
The model of Pedersen et al. (2020) assumes that investors pursue the highest possible
Sharpe ratio, subject to a target average ESG score. Using wt as the Nt × 1 portfolio weight
w′ s
vector, st as the Nt × 1 vector of ESG scores, define the average ESG score s̄ = s′ ιtNt . Their
t t
Proposition 3 expresses the optimal weights as
wP F P,t = Σ−1
t (µt + πt (st − ιNt s̄)) (7)
for the scalar πt defined in their paper, returns’ covariance matrix Σt , and returns’ mean
µt .13 This expression requires that the portfolio is net long, that is wt′ ιNt ≥ 0, so that the
average ESG score s̄ has a natural interpretation. Conveniently, we find that our model-
implied Markowitz portfolio is net long over our entire sample. Reminiscently, Pastor et al.
(2021b) derive optimal weights as
wP ST,t = Σ−1
t (µt + dst ) (8)
where the scalar d ≥ 0 is the investor’s “ESG taste.”14 Assume for the moment that “bad”
ESG is denoted by negative values in s: the PST weight reduces the effective expected return
for bad-ESG stocks. While (7) and (8) are clearly similar, some differences emerge when we
use them in Section 4.4 below.
Since we use the restricted model estimates for the screened tangency portfolios, we use
13
We set the investor’s relative risk-aversion parameter to equal 1.
14
Again, set relative risk-aversion to equal 1.
15the same estimates to give us the mean and covariance that (7) and (8) require. Therefore
µt = βt λ where λ is the K × 1 price of factor risk, which we estimate as the factor mean
since they are tradable. We use the factor decomposition of stocks’ covariance matrix,
for simplicity assuming the idiosyncratic return covariance matrix Σε is diagonal: hence,
Σt = βt Sβt′ + Σε .15
When we use wP F P and wP ST , we should note the units of the ESG score s. As noted above
in Section 2, we follow previous studies in normalizing the other firm characteristics to be
ranks translated to the [−0.5, 0.5] interval. So when using ESG measures in the model, we do
the same: at each time the median ESG score is 0, the minimum is −0.5, and the maximum
is 0.5. Therefore, for the Pedersen et al. (2020) wP F P we will want to consider s̄ in this
interval. For the Pastor et al. (2021b) wP ST , this scaling also seems appropriate: if a firm
has median ESG, then the value of snt = 0 in (8) implies no tilt from the Markowitz weight.
In this case, we will want to set d so that different values of snt do not lead to unreasonable
tilts away from the Markowitz weights. For instance, with d = 0.01 the expected return
is effectively shifted by ±0.5% monthly as the ESG moves from the median to an extreme,
which could be considered a large ESG adjustment—we consider different values of d in our
results below.
The portfolio formulae are defined only for nonmissing ESG scores. Therefore we consider
two ways of imputing missing ESG values. The first imputes missing data with the aver-
age/median ESG score each month, i.e. zero. A value of zero implies that a missing ESG
score necessarily contributes nothing to βn,t or αn,t . It also implies that, given that we don’t
see information about the firm, we assume its ESG score is average. Our second imputation
value is born from the idea that missing ESG information could actually be a negative ESG
signal about the firm—imputing an average ESG score might be far too positive. In the ab-
sence of evidence that the firm is performing well at ESG, it may instead be safer to assume
it is doing poorly. Therefore, we also consider the imputation of missing ESG scores with a
value of −0.5, the worst value possible on our transformed scale.
Returning to the ESG screens we discussed first, note that we can accomplish them without
having imputed missing data, but they are equivalent to screens in data where we have. If a
missing value is imputed to be −0.5, then that firm would be zeroed-out in the third screen.
If a missing value is imputed to be 0, then that firm is not zeroed out by any of the screens
in the p25 and p50 cut-offs.
15
For any firm in our data with fewer than ten monthly observations, we set its idiosyncratic variance
equal to the average idiosyncratic variance of all firms—this only affects a few hundred observations.
163.4 Including ESG in the model
Instead, we might suppose that ESG measures provide useful information for either αn,t or
βn,t , or both, and therefore affect optimal portfolio weights. There are two main routes
we take to including ESG measures into the IPCA model. The first route includes the ESG
measures into the firm characteristics zn,t and estimates Γβ (and Γα ) as in Kelly et al. (2019).
In this way, ESG is treated like any other firm characteristic and the estimated model is just
what was presented in Section 3.1.
The second route uses ESG and firm characteristics differentially in αn,t and βn,t . Denote
the ESG measures as Lζ × 1 vector ζn,t and other characteristics as zn,t . In this case, we
impose the following that αn,t = Γ′α ζn,t and βn,t = Γ′β zn,t and so the modified model is
rn,t+1 = Γ′α ζn,t + zn,t
′
Γβ ft+1 + εn,t+1 . (9)
This embodies the idea that ESG measures tell us about return-predicting mispricing, while
other firm characteristics tell us about aggregate risk exposure. This model is a modified
version of the unrestricted model above, and because zn,t and ζn,t are different from each
other we obtain modified versions of (2) and (3) along with a new first-order condition for
Γα :
−1
ft+1 = Γ′β Zt′ Zt Γβ Γ′β Zt′ (rt+1 − ζt Γα ) (2.1)
T −1
!−1 T −1 !
X X
′
vec(Γβ ) = ft+1 ft+1 ⊗ Zt′ Zt ft ⊗ [Zt′ rt+1 − Zt′ ζt Γα ] (3.1)
t=1 t=1
T −1
!−1 T −1
!
X X
Γα = ζt′ ζt ζt′ [rt+1 − Zt Γβ ft+1 ] (10)
t=1 t=1
′
for ζt the Nt × Lζ matrix stacking ζn,t . Note that we no longer need an identification
assumption for Γα and Γβ so long as there does not exist Q such that ζt = Zt Q for all t.16
As we have noted, there are many firm-month observations that have no ESG data available.
There is not a single obvious solution for dealing with the missing data; we therefore employ
two broad alternatives. The first alternative is to restrict attention to only those firm-months
where ESG data is available. This essentially treats ESG like the other characteristics, and
requires we observe everything in order for the firm-month to be in our data. The second
16
This follows because we are no longer able to subtract a constant K × 1 vector ξ from the latent factor
time series and add Γβ ξ to Γα while leaving the model’s fitted values unchanged.
17alternative is to impute missing values to either 0 or −0.5, as previously discussed. We
report all of these alternatives in our results below.
3.5 Non-systematic strategies
In the basic model (1), Kelly et al. (2019) define a non-systematic investment strategy called
a “pure-alpha portfolio”:
−1
wα,t = Zt (Zt′ Zt ) Γα . (11)
Recall that we impose Γ′α Γβ = 0: therefore Γα is a combination of characteristics that is
orthogonal to every risk exposure’s combination of characteristics. Moreover, this condition
ensures that wα,t is cross-sectionally orthogonal to all factors’ betas because
−1
βt′ wα,t = Γ′β Zt′ Zt (Zt′ Zt ) Γα = Γ′β Γα = 0.
Therefore the pure-alpha portfolio has no factor risk.
However, naively using the strategy in (11) with the modified model of (9) does not ensure
the portfolio avoids factor risk. Section 3.1 noted we need no identification condition to sep-
arately identify Γβ and Γα in (9), therefore the estimator does not impose any orthogonality
between the parameters—indeed, orthogonality is not even well-defined because Γβ has row
dimension L while Γα has a different row dimension Lζ .17 And since ζ and Z are distinct, if
we naively used (11) (i.e. swap out Z for ζ) we see that
−1 −1
βt′ ζt (ζt′ ζt ) Γα = Γ′β Zt′ ζt (ζt′ ζt ) Γα ̸= 0,
unless Zt′ ζt = 0.
Therefore, in the modified model of (9) we need a new construction in order to arrive at a
portfolio with no factor risk. As it is distinct from the pure-alpha portfolio construction but
achieving the same aim, we call this a “beta-neutral” portfolio:
wα⊥β,t = I − βt (βt′ βt )−1 βt′ αt = I − Zt Γβ (Γ′β Zt′ Zt Γβ )−1 Γ′β Zt′ ζt Γα .
(12)
Clearly it is the case that βt′ wα⊥β,t = 0 for every t, regardless of the value of Γα . Interpreting
wα⊥β,t , in order to construct a portfolio with no factor risk, one only uses the part of ζt
17
For example, suppose Lζ = 1 (as will be the case in Section 4): the only way the scalar Γα could be
said to be “orthogonal” to Γβ in any meaningful sense is when Γα = 0 and vector multiplication “becomes”
scalar multiplication; for Lζ > 1 we cannot even use this.
18that is cross-sectionally orthogonal to the factor betas. In the case where ζ contains ESG
measures, those measures can deliver mispricing only to the extent they are cross-sectionally
orthogonal with the instrumented betas.
Both pure-alpha and beta-neutral portfolios are constructed to answer the same question:
are there predictable returns that are not compensation for aggregate risk ? Of course, our
main focus is on the importance of ESG measures. In pure-alpha portfolios, we will see
if including ESG information affects whatever alpha is present from all the characteristics
together. In beta-neutral portfolios, we will see if ESG delivers an alpha on its own.
3.6 Estimation details
We include a constant as an instrument alongside the firm characteristics and use the five-
factor model as our benchmark, following Kelly et al. (2019). For ease of interpretation,
we rescale all portfolios’ annualized volatility to 10%. Of course, this has no effect on the
Sharpe ratios or t-statistics, and only serves to put the various portfolios’ means on the same
footing. All of our results come from in-sample estimation. Kelly et al. (2019) and Kelly
et al. (forthcoming) have shown that IPCA parameters are quite stable due to the great deal
of dimension reduction employed, with limited impact of in- versus out-of-sample estimation.
Moreover, our focus is really on the comparative static exercise of including versus ignoring
ESG scores: in-sample results give ESG measures the best chance of providing predictive
information.
4 Results
In this section we present our main results. We start by using ESG scores to tilt systematic
investment strategies. Then we consider the role of ESG measures in model estimation.
We consider the robustness of our results to many alternative specifications, and point to
comprehensive further analysis in the online appendix. Then we consider the properties
of well-performing ESG-tilted portfolios. Finally, we connect our empirical results to the
empirical literature, and also to a model of responsible investing.
194.1 ESG as a tilt
We assume the investor cares about an ESG-investing mandate for an exogenous reason,
regardless of whether or not ESG measures help predict returns. Nevertheless, the investor
retains a profit motive and uses the information at hand to form a profitable investment
strategy. Our question becomes: how costly is it to adjust a profitable investment strategy
to adhere to an ESG-investing mandate?
Given that Figure 2 shows that ESG measures are most widely available for large firms, we
focus our main attention on results for large firms. Our main results are in Table I. The
takeaway is that following an ESG mandate can have a very low cost, perhaps none at all,
in terms of investment performance. The top row reports the original tangency portfolio’s
performance from step 1. This portfolio is based on a five-factor IPCA model restricted to
large firms. The annualized Sharpe ratio is 1.46 (t = 2.30) and explains 31% of individual
stock returns. These R2 and tangency-portfolio Sharpe ratios are broadly in line with what
Kelly et al. (2019) report for large firms on their longer sample using different characteristics
and a different size cut-off. In the first column across a multitude of rows, we see that many
ESG-tilted strategies have essentially the same performance.
In Panel B we consider the KLD scores. If we simply zero-out firms with a below-median
(p50 ) ESG score, the tilted-tangency portfolio yields an annualized Sharpe ratio of 1.52 that
remains significant at the 5% level (t = 2.39), slightly higher than the original tangency
portfolio. This approach corresponds to ‘negative screening’, one of the most common im-
plementations of ESG investment mandates (Dimson et al., 2020). If we instead zero-out
below-median ESG only in the long-leg, the tilted-tangency portfolio has a mildly lower
Sharpe of 1.25 that remains significant (t = 1.97). Making the screen less-stringent at p25
has little effect when applied to both legs, but results in a smaller drop (to 1.43, t = 2.25)
when applied only to the long-leg. A more-stringent p75 screen deteriorates performance only
mildly when applied to both legs (to 1.39, t = 2.20) but is more deleterious when applied
only to the long-leg (0.78, t = 1.23). Hence, the portfolio is not immune to whatever change
implemented—of course, we wouldn’t expect it to be. But simple, reasonable screens deliver
portfolios that lose little-to-none of the original tangency portfolio’s profits. In the remain-
ing panels, zeroing-out below-median ESG leads to tilted-tangency portfolios with significant
Sharpe ratios of 1.34, 1.37, and 1.51 for the Asset4 (Panel C), Sustainalytics (Panel D), and
RepRisk (Panel E) ESG providers, respectively. Hence, the low costs of an ESG-mandate
tilt are common across the various measures.
If instead we keep only those firms with above median ESG (labeled “zero-out wtan,t not-
20Table I
ESG as a tilt
Notes – Annualized Sharpe ratio and mean, and excess kurtosis and skewness of the monthly returns,
for tangency portfolio and tilted portfolio returns. In parentheses are t-statistics: for Sharpe ratios from Lo
(2003), and for means from Newey and West (1987) with three lags. Portfolios scaled to have 10% annualized
volatility.
SR Mean Kurtosis Skewness
Panel A
Large 1.46 (2.30) 14.58 (7.29) 1.96 0.18
Panel B: KLD
Large, zero-out wtan,t below p25 ESG 1.48 (2.34) 14.79 (7.35) 2.36 0.46
Large, zero-out wtan,t below p50 ESG 1.52 (2.39) 15.15 (7.52) 3.86 0.76
Large, zero-out wtan,t below p75 ESG 1.39 (2.20) 13.90 (6.48) 6.24 1.10
Large, zero-out wtan,t below p25 ESG in long-leg 1.43 (2.25) 14.26 (7.06) 2.21 0.39
Large, zero-out wtan,t below p50 ESG in long-leg 1.25 (1.97) 12.49 (6.17) 2.76 0.19
Large, zero-out wtan,t below p75 ESG in long-leg 0.78 (1.23) 7.75 (3.78) 1.73 −0.00
Large, zero-out wtan,t not-above p25 ESG 1.07 (1.69) 10.67 (6.08) 2.31 −0.16
Large, zero-out wtan,t not-above p50 ESG 1.14 (1.81) 11.41 (6.71) 1.99 0.09
Large, zero-out wtan,t not-above p75 ESG 1.01 (1.59) 10.05 (5.68) 2.83 −0.39
Large, PFP optimal, missing ESG as 0, s̄ = 0 1.49 (2.25) 14.87 (7.25) 1.94 −0.03
Large, PFP optimal, missing ESG as 0, s̄ = −0.25 1.46 (2.20) 14.58 (7.08) 2.03 −0.01
Large, PFP optimal, missing ESG as 0, s̄ = 0.25 1.49 (2.25) 14.86 (7.26) 1.87 −0.05
Large, PFP optimal, missing ESG as −0.5, s̄ = 0 1.51 (2.28) 15.08 (7.44) 1.81 0.04
Large, PFP optimal, missing ESG as −0.5, s̄ = −0.25 1.49 (2.26) 14.92 (7.29) 1.91 −0.01
Large, PFP optimal, missing ESG as −0.5, s̄ = 0.25 1.51 (2.28) 15.04 (7.47) 1.73 0.08
Large, PST optimal, missing ESG as 0, d = 0.01 0.35 (0.56) 3.51 (1.85) 1.91 −0.29
Large, PST optimal, missing ESG as 0, d = 0.001 1.36 (2.15) 13.60 (7.11) 1.12 −0.16
Large, PST optimal, missing ESG as 0, d = 0.0001 1.49 (2.35) 14.89 (7.71) 1.83 −0.02
Large, PST optimal, missing ESG as −0.5, d = 0.01 0.17 (0.22) 1.70 (0.76) 0.25 0.05
Large, PST optimal, missing ESG as −0.5, d = 0.001 1.26 (2.00) 12.63 (6.95) 1.16 0.15
Large, PST optimal, missing ESG as −0.5, d = 0.0001 1.50 (2.36) 14.97 (7.81) 1.74 0.04
Panel C: Asset4
Large, zero-out wtan,t below p25 ESG 1.39 (2.19) 13.84 (6.70) 2.70 0.03
Large, zero-out wtan,t below p50 ESG 1.34 (2.12) 13.39 (6.29) 3.05 0.28
Large, zero-out wtan,t below p75 ESG 1.31 (2.06) 13.04 (5.99) 3.77 0.67
Large, zero-out wtan,t below p25 ESG in long-leg 1.40 (2.21) 13.98 (6.79) 2.33 0.37
Large, zero-out wtan,t below p50 ESG in long-leg 1.22 (1.93) 12.20 (5.84) 2.38 0.47
Large, zero-out wtan,t below p75 ESG in long-leg 0.96 (1.52) 9.62 (4.63) 1.75 0.23
Large, zero-out wtan,t not-above p25 ESG 0.68 (1.08) 6.83 (3.54) 6.61 0.19
Large, zero-out wtan,t not-above p50 ESG 0.59 (0.93) 5.85 (2.96) 7.47 0.25
Large, zero-out wtan,t not-above p75 ESG 0.51 (0.81) 5.14 (2.60) 6.00 −0.07
Large, PFP optimal, missing ESG as 0, s̄ = 0 1.18 (1.34) 11.74 (4.50) 1.51 −0.43
Large, PFP optimal, missing ESG as 0, s̄ = −0.25 1.16 (1.31) 11.53 (4.39) 1.43 −0.43
Large, PFP optimal, missing ESG as 0, s̄ = 0.25 1.17 (1.33) 11.71 (4.50) 1.68 −0.45
Large, PFP optimal, missing ESG as −0.5, s̄ = 0 1.19 (1.35) 11.85 (4.54) 1.68 −0.47
Large, PFP optimal, missing ESG as −0.5, s̄ = −0.25 1.16 (1.32) 11.60 (4.44) 1.56 −0.45
Large, PFP optimal, missing ESG as −0.5, s̄ = 0.25 1.20 (1.36) 11.94 (4.56) 1.84 −0.49
Large, PST optimal, missing ESG as 0, d = 0.01 0.36 (0.56) 3.55 (1.89) 3.88 −0.26
Large, PST optimal, missing ESG as 0, d = 0.001 1.36 (2.14) 13.54 (7.13) 1.59 −0.14
Large, PST optimal, missing ESG as 0, d = 0.0001 1.48 (2.34) 14.81 (7.68) 1.91 −0.02
Large, PST optimal, missing ESG as −0.5, d = 0.01 0.52 (0.58) 5.15 (1.83) 0.31 −0.20
Large, PST optimal, missing ESG as −0.5, d = 0.001 1.37 (2.17) 13.70 (7.01) 1.99 −0.25
Continued on next page
21SR Mean Kurtosis Skewness
Large, PST optimal, missing ESG as −0.5, d = 0.0001 1.49 (2.35) 14.87 (7.69) 1.95 −0.03
Panel D: Sustainalytics
Large, zero-out wtan,t below p25 ESG 1.42 (2.25) 14.22 (7.04) 2.04 0.19
Large, zero-out wtan,t below p50 ESG 1.37 (2.17) 13.71 (6.65) 2.32 0.23
Large, zero-out wtan,t below p75 ESG 1.33 (2.10) 13.31 (6.34) 2.70 0.30
Large, zero-out wtan,t below p25 ESG in long-leg 1.41 (2.22) 14.07 (6.90) 2.24 0.19
Large, zero-out wtan,t below p50 ESG in long-leg 1.31 (2.07) 13.06 (6.28) 2.36 0.24
Large, zero-out wtan,t below p75 ESG in long-leg 1.17 (1.85) 11.72 (5.59) 1.91 0.25
Large, zero-out wtan,t not-above p25 ESG 0.74 (1.17) 7.36 (3.84) 17.90 2.74
Large, zero-out wtan,t not-above p50 ESG 0.65 (1.02) 6.45 (3.40) 14.03 2.21
Large, zero-out wtan,t not-above p75 ESG 0.62 (0.97) 6.15 (3.05) 9.29 1.77
Large, PFP optimal, missing ESG as 0, s̄ = 0 1.86 (1.47) 18.49 (6.23) 0.75 0.17
Large, PFP optimal, missing ESG as 0, s̄ = −0.25 1.86 (1.47) 18.48 (6.12) 0.78 0.16
Large, PFP optimal, missing ESG as 0, s̄ = 0.25 1.83 (1.45) 18.24 (6.23) 0.68 0.19
Large, PFP optimal, missing ESG as −0.5, s̄ = 0 1.87 (1.48) 18.56 (6.34) 0.71 0.17
Large, PFP optimal, missing ESG as −0.5, s̄ = −0.25 1.86 (1.47) 18.53 (6.21) 0.72 0.13
Large, PFP optimal, missing ESG as −0.5, s̄ = 0.25 1.85 (1.47) 18.45 (6.40) 0.68 0.20
Large, PST optimal, missing ESG as 0, d = 0.01 0.48 (0.76) 4.82 (2.59) 6.46 −0.23
Large, PST optimal, missing ESG as 0, d = 0.001 1.42 (2.24) 14.20 (7.45) 1.53 0.01
Large, PST optimal, missing ESG as 0, d = 0.0001 1.48 (2.34) 14.83 (7.68) 1.88 −0.01
Large, PST optimal, missing ESG as −0.5, d = 0.01 0.16 (0.13) 1.63 (0.41) 0.35 0.02
Large, PST optimal, missing ESG as −0.5, d = 0.001 1.30 (2.05) 12.97 (6.68) 1.67 0.02
Large, PST optimal, missing ESG as −0.5, d = 0.0001 1.48 (2.33) 14.74 (7.63) 1.91 −0.01
Panel E: RepRisk
Large, zero-out wtan,t below p25 ESG 1.53 (2.42) 15.31 (7.63) 2.21 0.45
Large, zero-out wtan,t below p50 ESG 1.51 (2.38) 15.06 (7.33) 2.75 0.60
Large, zero-out wtan,t below p75 ESG 1.46 (2.31) 14.59 (6.99) 2.93 0.66
Large, zero-out wtan,t below p25 ESG in long-leg 1.50 (2.37) 15.01 (7.45) 2.20 0.45
Large, zero-out wtan,t below p50 ESG in long-leg 1.37 (2.17) 13.72 (6.61) 2.47 0.46
Large, zero-out wtan,t below p75 ESG in long-leg 1.26 (1.98) 12.55 (5.99) 2.17 0.44
Large, zero-out wtan,t not-above p25 ESG 0.65 (1.03) 6.53 (3.57) 8.57 0.86
Large, zero-out wtan,t not-above p50 ESG 0.62 (0.98) 6.17 (3.36) 7.03 0.35
Large, zero-out wtan,t not-above p75 ESG 0.50 (0.79) 5.01 (2.64) 9.99 0.35
Large, PFP optimal, missing ESG as 0, s̄ = 0 1.16 (1.14) 11.58 (3.87) 1.54 −0.50
Large, PFP optimal, missing ESG as 0, s̄ = −0.25 1.13 (1.11) 11.29 (3.75) 1.64 −0.54
Large, PFP optimal, missing ESG as 0, s̄ = 0.25 1.17 (1.15) 11.66 (3.90) 1.47 −0.48
Large, PFP optimal, missing ESG as −0.5, s̄ = 0 1.17 (1.15) 11.68 (3.90) 1.52 −0.49
Large, PFP optimal, missing ESG as −0.5, s̄ = −0.25 1.15 (1.13) 11.46 (3.82) 1.61 −0.52
Large, PFP optimal, missing ESG as −0.5, s̄ = 0.25 1.18 (1.16) 11.78 (3.94) 1.44 −0.47
Large, PST optimal, missing ESG as 0, d = 0.01 0.68 (0.91) 6.78 (2.61) 9.92 −0.79
Large, PST optimal, missing ESG as 0, d = 0.001 1.47 (2.31) 14.65 (7.65) 1.09 0.03
Large, PST optimal, missing ESG as 0, d = 0.0001 1.50 (2.36) 14.93 (7.73) 1.84 0.00
Large, PST optimal, missing ESG as −0.5, d = 0.01 −0.28 (−0.12) −2.78 (−0.33) −0.71 −0.22
Large, PST optimal, missing ESG as −0.5, d = 0.001 1.36 (2.14) 13.55 (6.86) 0.90 0.02
Large, PST optimal, missing ESG as −0.5, d = 0.0001 1.49 (2.35) 14.90 (7.71) 1.81 0.01
above p50 ”), we see worse outcomes.18 This is the case particularly for the ESG providers with
fewer observations (Asset4, Sustainalytics, and RepRisk). For these providers, the Sharpe
ratios more than halve and become insignificant. We generally see the portfolio’s kurtosis and
22You can also read
